David L Miller & Mark V Bravington
International Whaling Commission Scientific Committee 2017
Part I
\[ \hat{N} = \frac{\text{study area}}{\text{covered area}}\sum_{i=1}^n \frac{s_i}{\hat{p}_i} \]
“A design is an algorithm for laying down samplers in the survey area”
“A realization (from that algorithm) is called a survey plan”
Len Thomas (Talk @CREEM 2004)
Part II
Hedley and Buckland (2004)
Miller et al. (2013)
Taking the previous example…
\[ \mathbb{E}\left(n_j\right) = \color{red}{A_j}\color{blue}{\hat{p}_j} \color{green}{\exp}\left[\color{grey}{ \beta_0 + \sum_k s_k(z_{kj})} \right] \]
\( n_j\sim \) some count distribution
\[ \int_\mathbb{R} \left( \frac{\partial^2 s(x)}{\partial x^2}\right)^2 \text{d}x\\ \]
library(dsm)
# environmental covariates
dsm_env_tw <- dsm(count~s(Depth) + s(NPP) + s(SST),
ddf.obj=df_hr,
segment.data=segs, observation.data=obs,
family=tw())
# space
dsm_xy_tw <- dsm(count~s(x, y), ddf.obj=df_hr,
segment.data=segs, observation.data=obs,
family=tw())
dsm is based on mgcv by Simon Wood
NO
s(x,y) + s(Depth)dsmdsmPart III
Thanks to Hiroto Murase and co for this data!
Spatial models alone can't solve these issues
Spatial models alone can't solve these issues
Spatial models alone can't solve these issues
Part IV
ltdesigntester github.com/dill/ltdesigntesterDSsim by Laura Marshall, CREEM)bs="tp" (Wood, 2003)bs="ts" (Marra et al., 2011)bs="ds", m=c(1, 0.5) (Miller et al., 2014)library(ltdesigntester)
# setup a simulation
my_sim <- build_sim(design_path="path/to/shp",
dsurf=density_surface_matrix,
n_grid_x=dsurf_dim_x,
n_grid_y=dsurf_dim_y,
n_pop=true_N,
df=detection_function_specs,
region="path/to/shp")
# run it!
res <- do_sim(nsim=number_of_sims,
scenario=my_sim,
pred_dat=prediction_data_frame, ...)
list()Part V
k be? “Big enough”?gam.check gives useful output
gam.check(dsm_env_tw)
Method: REML Optimizer: outer newton
full convergence after 8 iterations.
Gradient range [-3.139726e-08,2.036272e-08]
(score 375.9503 & scale 4.316452).
Hessian positive definite, eigenvalue range [0.5725432,298.5906].
Model rank = 28 / 28
Basis dimension (k) checking results. Low p-value (k-index<1) may
indicate that k is too low, especially if edf is close to k'.
k' edf k-index p-value
s(Depth) 9.000 4.049 0.814 0.36
s(NPP) 9.000 2.846 0.779 0.04
s(SST) 9.000 4.916 0.771 0.04
“Everything is related to everything else, but near things are more related than distant things”
Tobler (1970)
mgcv::concurvity, dsm::vis.concurvity)dsm, obs_exp() does this> obs_exp(b, "beaufort")
1 2 34
Observed 3.00000 10.00000 80.00000
Expected 6.97715 12.42649 83.03773
> obs_exp(b_nc, "beaufort")
1 2 34
Observed 3.000000 10.00000 80.00000
Expected 8.478759 17.00705 73.23535
Slides w/ references available at converged.yt
\[ \mathbb{P} \left[ \text{animal detected } \vert \text{ animal at distance } y\right] = g(y;\boldsymbol{\theta}) \]
\[ \hat{p} = \frac{1}{w} \int_0^w g(y; \boldsymbol{\hat{\theta}}) \text{d}y \]
Figure from Marques et al (2007)

Picture from University of St Andrews Library Special Collections